Berdyshev, Abdumauvlen S.Cabada Fernández, AlbertoKarimov, Erkinjon T.2020-11-102020-11-102020Berdyshev, A.; Cabada, A.; Karimov, E. On the Existence of Eigenvalues of a Boundary Value Problem with Transmitting Condition of the Integral Form for a Parabolic-Hyperbolic Equation. Mathematics 2020, 8, 1030http://hdl.handle.net/10347/23638In the paper, we investigate a local boundary value problem with transmitting condition of the integral form for mixed parabolic-hyperbolic equation with non-characteristic line of type changing. Theorem on strong solvability of the considered problem has been proved and integral representation of the solution is obtained in a functional space. Using Lidskii Theorem on coincidences of matrix and spectral traces of nuclear operator and Gaal’s formula for evaluating traces of nuclear operator, which is represented as a product of two Hilbert-Schmidt operators, we prove the existence of eigenvalues of the considered problemeng© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/)Atribución 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/Transmitting conditionParabolic-hyperbolic equationGreen’s functionjournal article10.3390/math80610302227-7390open access